Approximatingq-order reduced density matrices in terms of the lower-order ones. II. Applications

The general equation linking a q-order reduced density matrix (q-RDM) with the corresponding q-order hole reduced density matrix (q-HRDM) has been reported in the preceding paper F. Colmenero, C. Perez del Valle, and C. Valdemoro, preceding paper, Phys. Rev. A 47, 971 (1993). In this equation, neither Kronecker functions nor mixed products of elements of RDM's and HRDM's appear, and the part involving hole terms has the same structure as that involving particle terms. Recently C. Valdemoro, Phys. Rev. A 45, 4462 (1992), a similar equation for q=2 has been used to approximate the 2-RDM from the knowledge of the 1-RDM. Here, the 3-RDM and the 4-RDM are approximated by using the 2-RDM as an initial datum. The ultimate aim of this research is to develop an iterative method for solving the contracted form of the Schr\"odinger equation L. Cohen and C. Frishberg, Phys. Rev. A 13, 927 (1976) ; H. Nakatsuji, ibid. 14, 41 (1976). A matrix form in the orbital representation of this equation is reported here. Finally, the second-order hypervirial equation, also in its matrix form, has been derived so that the quality of the results can be judged.